Liouville field theory and log-correlated Random Energy Models

Abstract

An exact mapping is established between the $c\ge 25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.

5 pages, 3 figures + 10 pages, 2 figures; accepted version

References in corpus (13)

• Anderson Transitions
• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• Duality and KPZ in Liouville Quantum Gravity
• Classical Particle in a Box with Random Potential: exploiting rotational symmetry of replicated Hamiltonian
• Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite dimensional Euclidean spaces
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• High values of disorder-generated multifractals and logarithmically correlated processes
• On an explicit construction of Parisi landscapes in finite dimensional Euclidean spaces
• On Barnes Beta Distributions and Applications to the Maximum Distribution of the 2D Gaussian Free Field
• On the genealogy of branching random walks and of directed polymers
• On the construction of the correlation numbers in Minimal Liouville Gravity
• One step replica symmetry breaking and extreme order statistics of logarithmic REMs
• Joint min-max distribution and Edwards-Anderson's order parameter of the circular $1/f$-noise model

Cited by in corpus (11)

• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Quantum Gravity from Timelike Liouville theory
• The DOZZ Formula from the Path Integral
• Statistics of extremes in eigenvalue-counting staircases
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Darcy's law of yield stress fluids on a treelike network
• Level Set Percolation in Two-Dimensional Gaussian Free Field
• Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions
• Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions
• On the analytical continuation of lattice Liouville theory